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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 715 · 40 questions
TalentJR

How to solve it (180 is the magic number): The three angles of a triangle add up to 180°. An exterior angle equals the sum of the two interior angles opposite it. An isosceles triangle has two equal angles, opposite its two equal sides. Angles on a straight line add up to 180°; vertically opposite angles are equal.

NameDateTime takenScore ___ / 40
  1. 1.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 115° (b) 105° (c) 140° (d) 65°
  2. 2.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 130° (b) 155° (c) 105° (d) 75°
  3. 3.Two angles of a triangle are 70° and 45°. What is the third angle? (a) 110° (b) 115° (c) 65° (d) 135°
  4. 4.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 40° (c) 130° (d) 50°
  5. 5.Two angles of a triangle are 35° and 135°. What is the third angle? (a) 170° (b) 145° (c) 10° (d) 45°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 50° (c) 70° (d) 40°
  7. 7.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 255° (b) 105° (c) 76° (d) 75°
  8. 8.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 65° (b) 90° (c) 155° (d) 115°
  9. 9.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 55° (b) 160° (c) 125° (d) 145°
  10. 10.Two angles of a triangle are 25° and 90°. What is the third angle? (a) 90° (b) 115° (c) 65° (d) 155°
  11. 11.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 30° (c) 60° (d) 120°
  12. 12.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 150° (b) 110° (c) 100° (d) 70°
  13. 13.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 90° (c) 45° (d) 135°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 46° (b) 90° (c) 45° (d) 135°
  15. 15.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 60° (b) 30° (c) 330° (d) 150°
  16. 16.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 40° (c) 220° (d) 140°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 70° (c) 80° (d) 160°
  18. 18.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 155° (b) 160° (c) 45° (d) 135°
  19. 19.Two angles of a triangle are 20° and 120°. What is the third angle? (a) 160° (b) 60° (c) 40° (d) 140°
  20. 20.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 125° (c) 70° (d) 35°
  21. 21.Two angles of a triangle are 50° and 25°. What is the third angle? (a) 155° (b) 105° (c) 75° (d) 130°
  22. 22.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 140° (b) 135° (c) 95° (d) 85°
  23. 23.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 275° (b) 95° (c) 85° (d) 5°
  24. 24.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 145° (b) 95° (c) 120° (d) 35°
  25. 25.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 120° (c) 60° (d) 30°
  26. 26.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 335° (b) 65° (c) 25° (d) 155°
  27. 27.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 170° (b) 100° (c) 10° (d) 90°
  28. 28.Two angles of a triangle are 50° and 95°. What is the third angle? (a) 145° (b) 35° (c) 130° (d) 85°
  29. 29.Two angles of a triangle are 30° and 55°. What is the third angle? (a) 125° (b) 85° (c) 95° (d) 150°
  30. 30.Two angles of a triangle are 50° and 70°. What is the third angle? (a) 110° (b) 120° (c) 130° (d) 60°
  31. 31.Two angles of a triangle are 55° and 90°. What is the third angle? (a) 90° (b) 125° (c) 35° (d) 145°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 20° (b) 21° (c) 40° (d) 160°
  33. 33.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 40° (b) 100° (c) 120° (d) 140°
  34. 34.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 230° (b) 130° (c) 50° (d) 115°
  35. 35.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 55° (c) 35° (d) 110°
  36. 36.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 215° (b) 145° (c) 36° (d) 35°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 105° (b) 150° (c) 76° (d) 75°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 120° (c) 60° (d) 30°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 170° (b) 20° (c) 10° (d) 11°
  40. 40.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 105° (b) 140° (c) 40° (d) 115°

Answer key

  1. 65°
  2. 75°
  3. 65°
  4. 130°
  5. 10°
  6. 70°
  7. 75°
  8. 115°
  9. 125°
  10. 65°
  11. 60°
  12. 70°
  13. 90°
  14. 45°
  15. 150°
  16. 40°
  17. 80°
  18. 135°
  19. 40°
  20. 70°
  21. 105°
  22. 95°
  23. 95°
  24. 145°
  25. 120°
  26. 155°
  27. 10°
  28. 35°
  29. 95°
  30. 60°
  31. 35°
  32. 20°
  33. 40°
  34. 130°
  35. 110°
  36. 35°
  37. 75°
  38. 30°
  39. 10°
  40. 40°

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